ICML 2025 论文列表

Machine learning is becoming an increasingly valuable tool in mathematics, enabling one to identify subtle patterns across collections of examples so vast that they would be impossible for a single researcher to feasibly review and analyze. In this work, we use graph neural networks to investigate quiver mutation---an operation that transforms one quiver (or directed multigraph) into another---which is central to the theory of cluster algebras with deep connections to geometry, topology, and physics. In the study of cluster algebras, the question of mutation equivalence is of fundamental concern: given two quivers, can one efficiently determine if one quiver can be transformed into the other through a sequence of mutations? In this paper, we use graph neural networks and AI explainability techniques to independently discover mutation equivalence criteria for quivers of type $\tilde{D}$. Along the way, we also show that even without explicit training to do so, our model captures structure within its hidden representation that allows us to reconstruct known criteria from type $D$, adding to the growing evidence that modern machine learning models are capable of learning abstract and general rules from mathematical data.

What algorithms do LLMs actually learn and use to solve problems? Studies addressing this question are sparse, as research priorities are focused on improving performance through scale, leaving a theoretical and empirical gap in understanding emergent algorithms. This position paper proposes AlgEval: a framework for systematic research into the algorithms that LLMs learn and use. AlgEval aims to uncover algorithmic primitives, reflected in latent representations, attention, and inference-time compute, and their algorithmic composition to solve task-specific problems. We highlight potential methodological paths and a case study toward this goal, focusing on emergent search algorithms. Our case study illustrates both the formation of top-down hypotheses about candidate algorithms, and bottom-up tests of these hypotheses via circuit-level analysis of attention patterns and hidden states. The rigorous, systematic evaluation of how LLMs actually solve tasks provides an alternative to resource-intensive scaling, reorienting the field toward a principled understanding of underlying computations. Such algorithmic explanations offer a pathway to human-understandable interpretability, enabling comprehension of the model's internal reasoning performance measures. This can in turn lead to more sample-efficient methods for training and improving performance, as well as novel architectures for end-to-end and multi-agent systems.

The Abstraction and Reasoning Corpus (ARC-AGI) poses a significant challenge for large language models (LLMs), exposing limitations in their abstract reasoning abilities. In this work, we leverage task-specific data augmentations throughout the training, generation, and scoring phases, and employ a depth-first search algorithm to generate diverse, high-probability candidate solutions. Furthermore, we utilize the LLM not only as a generator but also as a scorer, using its output probabilities to select the most promising solutions. Our method achieves a score of 71.6% (286.5/400 solved tasks) on the public ARC-AGI evaluation set, demonstrating state-of-the-art performance among publicly available approaches. While concurrent closed-source work has reported higher scores, our method distinguishes itself through its transparency, reproducibility, and remarkably low inference cost, averaging only around 2ct per task on readily available hardware.

We introduce Spatial Reasoning Models (SRMs), a framework to perform reasoning over sets of continuous variables via denoising generative models. SRMs infer continuous representations on a set of unobserved variables, given observations on observed variables. Current generative models on spatial domains, such as diffusion and flow matching models, often collapse to hallucination in case of complex distributions. To measure this, we introduce a set of benchmark tasks that test the quality of complex reasoning in generative models and can quantify hallucination. The SRM framework allows to report key findings about importance of sequentialization in generation, the associated order, as well as the sampling strategies during training. It demonstrates, for the first time, that order of generation can successfully be predicted by the denoising network itself. Using these findings, we can increase the accuracy of specific reasoning tasks from <1% to >50%. Our [project website](https://geometric-rl.mpi-inf.mpg.de/srm/) provides additional videos, code, and the benchmark datasets.

We present MILS: Multimodal Iterative LLM Solver, a surprisingly simple, training-free approach, to imbue multimodal capabilities into your favorite LLM. Leveraging their innate ability to perform multi-step reasoning, MILS prompts the LLM to generate candidate outputs, each of which are scored and fed back iteratively, eventually generating a solution to the task. This enables various applications that typically require training specialized models on task-specific data. In particular, we establish a new state-of-the-art on emergent zero-shot image, video and audio captioning. MILS seamlessly applies to media generation as well, discovering prompt rewrites to improve text-to-image generation, and even edit prompts for style transfer! Finally, being a gradient-free optimization approach, MILS can invert multimodal embeddings into text, enabling applications like cross-modal arithmetic.

Self-awareness, i.e., the ability to assess and correct one's generation, is a fundamental aspect of human intelligence, making its replication in large language models (LLMs) an important yet challenging task. Previous works tackle this by employing extensive reinforcement learning or relying on large external verifiers. In this work, we propose Refine via Intrinsic Self-Verification (ReVISE), an efficient and effective framework that enables LLMs to self-correct their outputs through self-verification. The core idea of ReVISE is to enable LLMs to verify their reasoning processes and continually rethink reasoning trajectories based on its verification. To implement this efficiently, we introduce a structured curriculum based on preference learning. Specifically, as ReVISE involves two challenging tasks (i.e., self-verification and reasoning correction), we tackle each task sequentially using curriculum learning, collecting both failed and successful reasoning paths to construct preference pairs for efficient training. During inference, our approach enjoys natural test-time scaling by integrating self-verification and correction capabilities, further enhanced by our proposed confidence-aware decoding mechanism. Our experiments on various reasoning tasks demonstrate that ReVISE achieves efficient self-correction and significantly improves the reasoning performance of LLMs.

Test-time training (TTT) methods explicitly update the weights of a model to adapt to the specific test instance, and they have found success in a variety of settings, including most recently language modeling and reasoning. To demystify this success, we investigate a gradient-based TTT algorithm for in-context learning, where we train a transformer model on the in-context demonstrations provided in the test prompt. Specifically, we provide a comprehensive theoretical characterization of linear transformers when the update rule is a single gradient step. Our theory (i) delineates the role of alignment between pretraining distribution and target task, (ii) demystifies how TTT can alleviate distribution shift, and (iii) quantifies the sample complexity of TTT including how it can significantly reduce the eventual sample size required for in-context learning. As our empirical contribution, we study the benefits of TTT for TabPFN, a tabular foundation model. In line with our theory, we demonstrate that TTT significantly reduces the required sample size for tabular classification (3 to 5 times fewer) unlocking substantial inference efficiency with a negligible training cost.

Modern large language models (LLMs) excel at fitting finetuning data, but often struggle on unseen examples. In order to teach models genuine reasoning abilities rather than superficial pattern matching, our work aims to better understand how the learning dynamics of LLM finetuning shapes downstream generalization. Our analysis focuses on reasoning tasks, whose problem structure allows us to distinguish between memorization (the exact replication of reasoning steps from the training data) and performance (the correctness of the final solution). We find that a model's performance on test prompts can be effectively characterized by a training metric we call pre-memorization train accuracy: the accuracy of model samples on training queries before they begin to copy the exact reasoning steps from the training set. On the dataset level, this metric is able to almost perfectly predict test accuracy, achieving $R^2$ of $\geq 0.9$ across various models (Llama3 8B, Gemma2 9B), datasets (GSM8k, MATH), and training configurations. On a per-example level, this metric is also indicative of whether individual model predictions are robust to perturbations in the training query. By connecting a model's learning dynamics to test performance, pre-memorization train accuracy can inform training decisions, such as the makeup of the training data. Our experiments on data curation show that prioritizing examples with low pre-memorization accuracy leads to 1.5-2x improvements in data efficiency compared to i.i.d. data scaling and other data scaling techniques.

In this paper, we aim to establish a simple, effective, and theoretically grounded benchmark for rigorously probing abstract reasoning in Large Language Models (LLMs). To achieve this, we first develop a mathematic framework that defines abstract reasoning as the ability to: (i) extract essential patterns independent of surface representations, and (ii) apply consistent rules to these abstract patterns. Based on this framework, we introduce two novel complementary metrics: Γ measures basic reasoning accuracy, while ∆ quantifies a model's reliance on specific symbols rather than underlying patterns - a key indicator of true abstraction versus mere memorization. To implement this measurement, we design a benchmark: systematic symbol remapping in rule-based tasks, which forces models to demonstrate genuine pattern recognition beyond superficial token matching. Extensive LLM evaluations using this benchmark (commercial API models, 7B-70B, multi-agent) reveal:1) critical limitations in non-decimal arithmetic and symbolic reasoning; 2) persistent abstraction gaps despite chain-of-thought prompting; and 3) ∆'s effectiveness in robustly measuring memory dependence by quantifying performance degradation under symbol remapping, particularly highlighting operand-specific memorization. These findings underscore that current LLMs, despite domain-specific strengths, still lack robust abstract reasoning, highlighting key areas for future improvement.

Despite substantial advances in scaling test-time compute, an ongoing debate in the community is how it should be scaled up to enable continued and efficient improvements with scaling. There are largely two approaches: (i) distilling successful search or thinking traces; and (ii), using verification (e.g., 0/1 outcome rewards, or verifiers) to guide reinforcement learning (RL) and search algorithms. In this paper, we prove that finetuning LLMs with verifier-based (VB) methods based on RL or search is far superior to verifier-free (VF) approaches based on distilling or cloning search traces, given a fixed amount of compute/data budget. Further, we show that as we scale test-time compute (measured as the output token length) and training data, suboptimality of VF methods scales poorly compared to VB when the base pre-trained LLM presents a heterogeneous distribution over correct solution traces (e.g., different lengths, styles, etc.) and admits a non-sharp distribution over rewards on traces sampled from it. We formalize this condition using anti-concentration [Erdős 1945], implying a stronger result that VB methods scale better asymptotically, with the performance gap between VB and VF widening as test-time budget grows. We corroborate our theory empirically on didactic and math reasoning problems with 3/8/32B-sized pre-trained LLMs, where we find verification is crucial for scaling test-time compute.

Language models (LMs) have shown impressive performance on tasks within their training distribution, but often struggle with structurally novel tasks even when given a small number of in-context task examples. We investigate the effectiveness of test-time training (TTT)—temporarily updating model parameters during inference using a loss derived from input data—as a mechanism for improving LMs' reasoning and few-shot learning capabilities. On the Abstraction and Reasoning Corpus (ARC), performing TTT with in-context examples yields up to $6\times$ higher accuracy compared to fine-tuned baselines—reaching $53.0\%$ on the public validation set with an 8B-parameter LM and $61.9\%$ when ensembled with program-synthesis methods, matching average human performance. On BIG-Bench Hard (BBH), TTT on in-context examples surpasses standard few-shot prompting in the $10$-shot setting by $7.3$ percentage points ($50.5\%$ to $57.8\%$). Our findings highlight the limitations of in-context learning for novel tasks and demonstrate the potential of test-time training to enhance language model adaptability.

As large language models (LLMs) are becoming more capable and widespread, the study of their failure cases is becoming increasingly important. Recent advances in standardizing, measuring, and scaling test-time compute suggest new methodologies for optimizing models to achieve high performance on hard tasks. In this paper, we apply these advances to the task of model jailbreaking: eliciting harmful responses from aligned LLMs. We develop an adversarial reasoning approach to automatic jailbreaking that leverages a loss signal to guide the test-time compute, achieving SOTA attack success rates against many aligned LLMs, even those that aim to trade inference-time compute for adversarial robustness. Our approach introduces a new paradigm in understanding LLM vulnerabilities, laying the foundation for the development of more robust and trustworthy AI systems.

Ensuring the safety and harmlessness of Large Language Models (LLMs) has become equally critical as their performance in applications. However, existing safety alignment methods typically suffer from safety-performance trade-offs and susceptibility to jailbreak attacks, primarily due to their reliance on direct refusals for malicious queries. In this paper, we propose **STAIR**, a novel framework that integrates **S**afe**T**y **A**lignment with **I**trospective **R**easoning. We enable LLMs to identify safety risks through step-by-step analysis by self-improving chain-of-thought (CoT) reasoning with safety awareness. STAIR first equips the model with a structured reasoning capability and then advances safety alignment via iterative preference optimization on step-level reasoning data generated using our newly proposed Safety-Informed Monte Carlo Tree Search (SI-MCTS). Specifically, we design a theoretically grounded reward for outcome evaluation to seek balance between helpfulness and safety. We further train a process reward model on this data to guide test-time searches for improved responses. Extensive experiments show that STAIR effectively mitigates harmful outputs while better preserving helpfulness, compared to instinctive alignment strategies. With test-time scaling, STAIR achieves a safety performance comparable to Claude-3.5 against popular jailbreak attacks. We have open-sourced our code, datasets and models at https://github.com/thu-ml/STAIR.

Structured image understanding, such as interpreting tables and charts, requires strategically refocusing across various structures and texts within an image, forming a reasoning sequence to arrive at the final answer. However, current multimodal large language models (LLMs) lack this multihop selective attention capability. In this work, we introduce ReFocus, a simple yet effective framework that equips multimodal LLMs with the ability to generate ``visual thoughts'' by performing visual editing on the input image through code, shifting and refining their visual focuses. Specifically, ReFocus enables multimodal LLMs to generate Python codes to call tools and modify the input image, sequentially drawing boxes, highlighting sections, and masking out areas, thereby enhancing the visual reasoning process. We experiment upon a wide range of structured image understanding tasks involving tables and charts. ReFocus largely improves performance on all tasks over GPT-4o without visual editing, yielding an average gain of 11.0% on table tasks and 6.8% on chart tasks. We present an in-depth analysis of the effects of different visual edits, and reasons why ReFocus can improve the performance without introducing additional information. Further, we collect a 14k training set using ReFocus, and prove that such visual chain-of-thought with intermediate information offers a better supervision than standard VQA data, reaching a 8.0% average gain over the same model trained with QA pairs and 2.6% over CoT.

Large Language Models (LLMs) exhibit strong potential in mathematical reasoning, yet their effectiveness is often limited by a shortage of high-quality queries. This limitation necessitates scaling up computational responses through self-generated data, yet current methods struggle due to spurious correlated data caused by ineffective exploration across all reasoning stages. To address such challenge, we introduce **MARGE**: Improving **Ma**th **R**easoning with **G**uided **E**xploration, a novel method that enhances mathematical reasoning through hit-guided exploration. MARGE systematically explores intermediate reasoning states derived from self-generated solutions, enabling adequate exploration and improved credit assignment throughout the reasoning process. Notably, MARGE improves both single-shot accuracy and exploration diversity, mitigating a common trade-off in alignment methods. These results demonstrate MARGE's effectiveness in enhancing mathematical reasoning capabilities and unlocking the potential of scaling self-generated training data.

Answering questions with Chain-of-Thought (CoT) has significantly enhanced the reasoning capabilities of Large Language Models (LLMs), yet its impact on Large Multimodal Models (LMMs) still lacks a systematic assessment and in-depth investigation. In this paper, we introduce **MME-CoT**, a specialized benchmark evaluating the CoT reasoning performance of LMMs, spanning six domains: math, science, OCR, logic, space-time, and general scenes. As the first comprehensive study in this area, we propose a thorough evaluation suite incorporating three novel metrics that assess the reasoning quality, robustness, and efficiency at a fine-grained level. Leveraging curated high-quality data and a unique evaluation strategy, we conduct an in-depth analysis of state-of-the-art LMMs, uncovering several key insights: *1)* Models with reflection mechanism demonstrate a superior CoT quality, with Kimi k1.5 outperforming GPT-4o and demonstrating the highest quality results; *2)* CoT prompting often degrades LMM performance on perception-heavy tasks, suggesting a potentially harmful overthinking behavior; and *3)* Although the CoT quality is high, LMMs with reflection exhibit significant inefficiency in both normal response and self-correction phases. We hope MME-CoT serves as a foundation for advancing multimodal reasoning in LMMs.

Self-evolving training—where models iteratively learn from their own outputs—has emerged as a key approach for complex reasoning tasks, addressing the scarcity of high-quality chain-of-thought data. However, its effectiveness in multimodal reasoning, a domain more intricate than text-only reasoning, remains underexplored, and the understanding of critical factors in this training paradigm remains limited. Furthermore, a central challenge for this training method is performance saturation, which impedes further improvements and scalability. Inspired by reinforcement learning (RL), in this paper, we reframe self-evolving training for multimodal reasoning through the lens of RL, identifying three pivotal factors: $\textit{Training Method}$, $\textit{Reward Model}$, and $\textit{Prompt Variation}$. Through systematic analysis, we establish relatively optimal design principles that significantly enhance multimodal reasoning capabilities. Moreover, delving deeper into training dynamics, we uncover the roots of saturation and propose a new automatic balancing mechanism to mitigate this limitation. Building on these insights, we propose M-STaR (**M**ultimodal **S**elf-evolving **T**r**a**ining for **R**easoning), a framework that achieves consistent performance gains across models of varying sizes and diverse benchmarks. All resources will be made publicly available.

The ideal AI safety moderation system would be both structurally interpretable (so its decisions can be reliably explained) and steerable (to align to safety standards and reflect a community's values), which current systems fall short on. To address this gap, we present SafetyAnalyst, a novel AI safety moderation framework. Given an AI behavior, SafetyAnalyst uses chain-of-thought reasoning to analyze its potential consequences by creating a structured "harm-benefit tree," which enumerates harmful and beneficial *actions* and *effects* the AI behavior may lead to, along with *likelihood*, *severity*, and *immediacy* labels that describe potential impacts on *stakeholders*. SafetyAnalyst then aggregates all effects into a harmfulness score using 28 fully interpretable weight parameters, which can be aligned to particular safety preferences. We applied this framework to develop an open-source LLM prompt safety classification system, distilled from 18.5 million harm-benefit features generated by frontier LLMs on 19k prompts. On comprehensive benchmarks, we show that SafetyAnalyst (average F1=0.81) outperforms existing moderation systems (average F1$<$0.72) on prompt safety classification, while offering the additional advantages of interpretability, transparency, and steerability.

Large language models (LLMs) are increasingly used for long-content generation (e.g., long Chain-of-Thought reasoning) where decoding efficiency becomes a critical bottleneck: Autoregressive decoding is inherently limited by its sequential token generation process, where each token must be generated before the next can be processed. This sequential dependency restricts the ability to fully leverage modern hardware’s parallel processing capabilities. Existing methods like speculative decoding and layer skipping offer potential speedups but have notable drawbacks: speculative decoding relies on an auxiliary “drafter” model, which can be challenging to acquire and increases memory overhead, while layer skipping may introduce discrepancies in the generated outputs due to the missing key-value cache at skipped layers. In this work, we propose AdaDecode, which accelerates LLM decoding without requiring auxiliary models or changes to the original model parameters, while ensuring output consistency. AdaDecode leverages the insight that many tokens—particularly simple or highly-predictable ones—can accurately be generated at intermediate layers, as further layers often do not significantly alter predictions once the model reaches a certain confidence. By adaptively generating tokens at intermediate layers when confidence is high, AdaDecode enables the next token’s computation to begin immediately. The remaining layer computations for early-predicted tokens are deferred and executed in parallel with subsequent tokens when needed, maximizing hardware utilization and reducing decoding latency. A final verification step ensures that early predictions match the results of standard autoregressive decoding, preserving output parity. Experiments across diverse generation tasks shows that AdaDecode consistently achieves superior decoding throughput compared to baselines with up to 1.73$\times$ speedup, while guaranteeing output parity with standard autoregressive decoding.